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@article{2017arXiv170602801P,
author = {Pachl, Jan and S{\'a}nchez Terraf, Pedro},
title = {Semipullbacks of labelled {M}arkov processes},
journal = {Logical Methods in Computer Science},
volume = 17,
number = 2,
year = 2021,
month = apr,
archive = {arXiv},
eprint = {1706.02801},
primaryclass = {math.PR},
keywords = {Mathematics - Probability, Computer Science - Logic in Computer Science, 28A35, 28A60, 68Q85, F.4.1, F.1.2},
zbl = {07350769},
adsurl = {http://adsabs.harvard.edu/abs/2017arXiv170602801P},
adsnote = {Provided by the SAO/NASA Astrophysics Data System},
doi = {10.23638/LMCS-17(2:3)2021},
url = {https://lmcs.episciences.org/7361},
abstract = {A \emph{labelled Markov process (LMP)} consists of a measurable
space $S$ together with an indexed family of Markov kernels from $S$
to itself. This structure has been used to model probabilistic
computations in Computer Science, and one of the main problems in
the area is to define and decide whether two LMP $S$ and $S'$ ``behave
the same''. There are two natural categorical definitions of
sameness of behavior: $S$ and $S'$ are \emph{bisimilar}
if there exist an LMP $ T$ and measure preserving maps
forming a diagram of the shape
$ S\leftarrow T \rightarrow{S'}$; and they
are \emph{behaviorally equivalent}
if there exist some $ U$ and maps forming a dual diagram
$ S\rightarrow U \leftarrow{S'}$.
These two notions differ for general measurable spaces but Edalat
proved that they coincide for analytic Borel spaces, showing that
from every
diagram $ S\rightarrow U \leftarrow{S'}$ one can obtain a
bisimilarity diagram as above. Moreover, the resulting square of
measure preserving maps is commutative (a \emph{semipullback}).
In this paper, we extend Edalat's result to measurable spaces $S$
isomorphic to a universally measurable subset of
a Polish space with the trace of the Borel $\sigma$-algebra, using a
version of Strassen's theorem on
common extensions of finitely additive measures.}
}
@article{minimal-dual-quasi,
author = {Caicedo, Xavier and Campercholi, Miguel and Kearnes, Keith A. and S{\'a}nchez Terraf, Pedro and Szendrei, {\'A}gnes and Vaggione, Diego},
year = 2021,
title = {Every minimal dual discriminator variety is minimal as a quasivariety},
journal = {Algebra universalis},
month = apr,
day = 29,
volume = 82,
number = 2,
pages = 36,
zbl = {1485.08005},
abstract = {Let $\dagger$ denote the following property of a variety $\mathcal{V}$: \emph{Every subquasivariety of $\mathcal{V}$ is a variety}. In this paper, we prove that every idempotent dual discriminator variety has property $\dagger$ . Property $\dagger$ need not hold for nonidempotent dual discriminator varieties, but $\dagger$ does hold for \emph{minimal} nonidempotent dual discriminator varieties. Combining the results for the idempotent and nonidempotent cases, we obtain that every minimal dual discriminator variety is minimal as a quasivariety},
issn = {1420-8911},
doi = {10.1007/s00012-021-00715-8},
url = {https://doi.org/10.1007/s00012-021-00715-8}
}
@article{moroni2020zhou,
title = {The {Z}hou Ordinal of Labelled {M}arkov Processes over Separable Spaces},
author = {Moroni, Martín Santiago and S\'anchez Terraf, Pedro},
journal = {The Review of Symbolic Logic},
month = dec,
year = 2023,
volume = 16,
number = 4,
pages = {1011--1032},
eprint = {2005.03630},
archive = {arXiv},
primaryclass = {cs.LO},
doi = {10.1017/S1755020322000375},
url = {https://doi.org/10.1017/S1755020322000375},
abstract = {There exist two notions of equivalence of behavior between states of a
Labelled Markov Process (LMP): state bisimilarity and event bisimilarity. The
first one can be considered as an appropriate generalization to continuous
spaces of Larsen and Skou's probabilistic bisimilarity, while the second one is
characterized by a natural logic. C. Zhou expressed state bisimilarity as the
greatest fixed point of an operator $\mathcal{O}$, and thus introduced an
ordinal measure of the discrepancy between it and event bisimilarity. We call
this ordinal the "Zhou ordinal" of $\mathbb{S}$, $\mathfrak{Z}(\mathbb{S})$.
When $\mathfrak{Z}(\mathbb{S})=0$, $\mathbb{S}$ satisfies the Hennessy-Milner
property. The second author proved the existence of an LMP $\mathbb{S}$ with
$\mathfrak{Z}(\mathbb{S}) \geq 1$ and Zhou showed that there are LMPs having an
infinite Zhou ordinal. In this paper we show that there are LMPs $\mathbb{S}$
over separable metrizable spaces having arbitrary large countable
$\mathfrak{Z}(\mathbb{S})$ and that it is consistent with the axioms of
$\mathit{ZFC}$ that there is such a process with an uncountable Zhou ordinal.}
}
@article{2022arXiv221015609G,
author = {Gunther, Emmanuel and Pagano, Miguel and S{\'a}nchez Terraf, Pedro and Steinberg, Mat{\'i}as},
title = {The formal verification of the ctm approach to forcing},
journal = {Annals of Pure and Applied Logic},
issn = {0168-0072},
url = {https://www.sciencedirect.com/science/article/pii/S0168007224000101},
keywords = {forcing, Isabelle/ZF, countable transitive models, continuum hypothesis, proof assistants, interactive theorem provers, generic extension},
year = 2024,
volume = 175,
month = may,
number = 5,
archiveprefix = {arXiv},
eprint = {2210.15609},
primaryclass = {math.LO},
adsurl = {https://ui.adsabs.harvard.edu/abs/2022arXiv221015609G},
adsnote = {Provided by the SAO/NASA Astrophysics Data System},
doi = {10.1016/j.apal.2024.103413},
abstract = {We discuss some highlights of our computer-verified proof of the construction, given a
countable transitive set-model $M$ of $\mathit{ZFC}$, of generic extensions satisfying
$\mathit{ZFC} + \neg\mathit{CH}$ and $\mathit{ZFC} + \mathit{CH}$. Moreover, let
$\mathcal{R}$ be the set of instances of the Axiom of Replacement. We isolated a
21-element subset $\Omega\subseteq\mathcal{R}$ and defined $\mathcal{F}:\mathcal
{R}\to\mathcal{R}$ such that for every $\Phi\subseteq\mathcal{R}$ and $M $-generic $G$,
$M\models \mathit{ZC} \cup \mathcal{F}\text{``}\Phi \cup \Omega$ implies
$M[G]\models \mathit{ZC} \cup \Phi \cup \{\neg\mathit{CH}\}$,
where $\mathit{ZC}$ is Zermelo set theory with Choice.
To achieve this, we worked in the proof assistant \emph{Isabelle},
basing our development on the Isabelle/ZF library by L.~Paulson and
others.}
}
@article{ciem40,
title = {Set Theory in {C}\'ordoba},
author = {S{\'a}nchez Terraf, Pedro},
year = 2024,
journal = {Actas de la Academia Nacional de Ciencias},
url = {preprints/CIEM40_sanchezterraf.pdf},
note = {In press. Extended abstract for invited talk at the 40th
anniversary of the Center for Research and Studies in
Mathematics (C\'ordoba)},
publisher = {Academia Nacional de Ciencias},
address = {Córdoba, Argentina},
abstract = { Set Theory is a new research area in Argentina, still with very few
practitioners.
We present some of the first steps towards its development at the
National University of C\'ordoba.
Cantor's \emph{continuum problem}, that of the determining which place
does the cardinality of the reals occupy in the cardinal line,
provides an appropriate frame for this exposition (and for the whole
of Set Theory indeed).}
}
@article{moroni2024classification,
title = {A classification of bisimilarities for general {M}arkov decision processes},
author = {Moroni, Mart{\'\i}n Santiago and S{\'a}nchez Terraf, Pedro},
year = {2024},
month = jan,
eprint = {2401.09273},
archiveprefix = {arXiv},
primaryclass = {cs.LO},
abstract = { We provide a fine classification of
bisimilarities between states of possibly different labelled Markov
processes (LMP). We show
that a bisimilarity relation proposed by Panangaden that uses direct sums coincides with ``event
bisimilarity'' from his joint work with Danos, Desharnais, and
Laviolette. We also extend Giorgio Bacci's notions of
bisimilarity between two different processes to the case of
nondeterministic LMP and generalize the game characterization of state
bisimilarity by Clerc et al. for the latter.}
}
@article{2024arXiv240407877K,
author = {{Kuperman}, Joel and {Petrovich}, Alejandro and S{\'a}nchez Terraf, Pedro},
title = {Definability of band structures on posets},
journal = {arXiv e-prints},
keywords = {Mathematics - Logic, Mathematics - Rings and Algebras},
year = 2024,
month = apr,
eid = {arXiv:2404.07877},
archiveprefix = {arXiv},
eprint = {2404.07877},
primaryclass = {math.LO},
adsurl = {https://ui.adsabs.harvard.edu/abs/2024arXiv240407877K},
adsnote = {Provided by the SAO/NASA Astrophysics Data System},
abstract = {The idempotent semigroups (bands) that give rise to partial orders by defining
$a \leq b \Leftrightarrow a \cdot b = a$ are the \emph{right-regular} bands (RRB), which are
axiomatized by $x\cdot y \cdot x = y \cdot x$. In this work we consider the
class of \emph{associative posets}, which comprises all partial orders
underlying right-regular bands, and study to what extent the ordering
determines the possible “compatible” band structures and their canonicity.
We show that the class of
associative posets in the signature $\{\leq\}$ is not first-order
axiomatizable. We also show that the Axiom of Choice is equivalent over $\mathit{ZF}$
to the fact that every tree with finite branches is associative. We also
present an adjunction between the categories of RRBs and that of associative
posets.
We study the smaller class of “normal” posets (corresponding to right-normal
bands) and give a structural characterization.
As an application of the order-theoretic perspective on bands, we generalize
results by the third author, obtaining “inner” direct product
representations for RRBs having a central (commuting) element.}
}
@misc{chain_bounding,
title = {{Chain Bounding} and the leanest proof of {Zorn}'s lemma},
author = {Incatasciato, Guillermo L. and S{\'a}nchez Terraf, Pedro},
year = 2024,
url = {preprints/chain_bounding.pdf},
note = {Expository article},
keywords = {Mathematics - Logic, Mathematics - History and Overview},
year = 2024,
month = apr,
eid = {arXiv:2404.11638},
archiveprefix = {arXiv},
eprint = {2404.11638},
primaryclass = {math.LO},
adsurl = {https://ui.adsabs.harvard.edu/abs/2024arXiv240411638I},
adsnote = {Provided by the SAO/NASA Astrophysics Data System},
abstract = {We present an exposition of the \emph{Chain Bounding Lemma}, which is a common
generalization of both Zorn's Lemma and the Bourbaki-Witt fixed point theorem.
The proofs of these results through the use of Chain Bounding are amongst the
simplest ones that we are aware of. As a by-product, we show that for every
poset $P$ and a function $f$ from the powerset of $P$ into $P$, there exists a
maximal well-ordered chain whose family of initial segments is appropriately closed
under $f$.
We also provide a “computer formalization” of our main results using the Lean
proof assistant.}
}
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