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@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 at {C}\'ordoba},
author = {S{\'a}nchez Terraf, Pedro},
pages = {61--65},
volume = 16,
month = jul,
year = 2024,
journal = {Actas de la Academia Nacional de Ciencias},
url = {https://www.anc-argentina.org.ar/wp-content/uploads/sites/36/2024/07/ANC_XVI.pdf},
note = {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{2024arXiv240407877K,
author = {{Kuperman}, Joel and {Petrovich}, Alejandro and S{\'a}nchez Terraf, Pedro},
title = {Definability of band structures on posets},
journal = {Semigroup Forum},
keywords = {Mathematics - Logic, Mathematics - Rings and Algebras},
year = 2024,
month = oct,
eid = {arXiv:2404.07877},
archiveprefix = {arXiv},
eprint = {2404.07877},
primaryclass = {math.LO},
url = {https://rdcu.be/dWI47},
doi = {10.1007/s00233-024-10477-z},
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 study the smaller class of “normal” posets (corresponding to right-normal
bands) and give a structural characterization.}
}
@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.}
}
@misc{chain_bounding,
title = {{Chain Bounding}, the leanest proof of {Zorn}'s lemma, and an
illustration of computerized proof formalization},
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 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 an introduction to the process of “computer formalization” of
mathematical proofs by using proofs assistants. As an illustration, we verify our main
results with the Lean proof assistant.}
}
@misc{elecccion_definible_cubo,
title = {Una aplicación de selectores definibles a los procesos de decisión de {Markov}},
author = {S{\'a}nchez Terraf, Pedro},
year = 2024,
url = {preprints/eleccion_definible_cubo_2024.pdf},
note = {In Spanish / en español},
keywords = {procesos de decisión de Markov, Teorema de Kuratowski y Ryll-Nardzewski},
year = 2024,
month = oct,
abstract = {En este trabajo pasamos revista al uso, en Ciencias de la Computación, de los
procesos de decisión de Markov sobre espacios de Borel estándares (i.e., que
provienen de espacios separables y completamente metrizables). Mostramos cómo
el Teorema de Selección de Kuratowski y Ryll-Nardzewski se utiliza para
demostrar la existencia de “planificadores” (\textit{schedulers})
medibles Borel. Estos permiten dar una representación determinista de sistemas
que admiten comportamientos probabilistas diversos para cada estado en el
que se encuentran.}
}
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