Related papers: Forcing the $\Pi^1_n$-Uniformization Property
A new axiom is proposed, the Ground Axiom, asserting that the universe is not a nontrivial set-forcing extension of any inner model. The Ground Axiom is first-order expressible, and any model of ZFC has a class-forcing extension which…
A topological constraint on the possible values of the universal quantization parameter is revealed in the case of geometric quantization on (boundary) curves diffeomorphic to $S^1$, analytically extended on a bounded domain in…
It is known that the set of possible cofinalities $\mathrm{pcf}(A)$ has good properties if $A$ is a progressive interval of regular cardinals. In this paper, we give an interval of regular cardinals $A$ such that $\mathrm{pcf}(A)$ has no…
This paper makes significant progress towards resolving a conjecture relating strong forcing axioms like $PFA$ and the derived model at a limit of Woodin cardinals $\kappa$. In particular, using a concept called Covering Matrices, we show…
With every $\sigma$-ideal $I$ on a Polish space we associate the $\sigma$-ideal $I^*$ generated by the closed sets in $I$. We study the forcing notions of Borel sets modulo the respective $\sigma$-ideals $I$ and $I^*$ and find connections…
The purpose of this work is two fold. Working in the framework of $(1+1)D$ Lorentz violating field theories we will investigate in the first place the general claim that fermionic interactions may be equivalent to a deformation of the…
We use a recently found parametrization of the solutions of the inverse Frobenius-Perron problem within the class of complete unimodal maps to develop a Monte-Carlo approach for the construction of one-dimensional chaotic dynamical laws…
A set of reals is \textit{universally Baire} if all of its continuous preimages in topological spaces have the Baire property. $\sf{Sealing}$ is a type of generic absoluteness condition introduced by Woodin that asserts in strong terms that…
Uniform interpolation properties are defined for equational consequence in a variety of algebras and related to properties of compact congruences on first the free and then the finitely presented algebras of the variety. It is also shown,…
We prove the following result which is due to the third author. Let $n \geq 1$. If $\boldsymbol\Pi^1_n$ determinacy and $\Pi^1_{n+1}$ determinacy both hold true and there is no $\boldsymbol\Sigma^1_{n+2}$-definable $\omega_1$-sequence of…
Recent advances in programming languages study and design have established a standard way of grounding computational systems representation in category theory. These formal results led to a better understanding of issues of control and…
If we replace first order logic by second order logic in the original definition of G\"odel's inner model $L$, we obtain HOD. In this paper we consider inner models that arise if we replace first order logic by a logic that has some, but…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
The construction and general implications of a model with complete supersymmetric unification of the Standard Model matter content, interactions and families' replication into a single $E_{8}$ gauge superfield in ten dimensions is…
A unified construction of canonical $H^m$-nonconforming finite elements is developed for $n$-dimensional simplices for any $m, n \geq 1$. Consistency with the Morley-Wang-Xu elements [Math. Comp. 82 (2013), pp. 25-43] is maintained when $m…
Providing explanations about how machine learning algorithms work and/or make particular predictions is one of the main tools that can be used to improve their trusworthiness, fairness and robustness. Among the most intuitive type of…
We prove a theorem on iterated forcing that can be used for preservation of $\aleph_2$ and $\aleph_1$ in iterations with supports of size $\aleph_1$ of forcings that have amalgamation properties similar to those present in the perfect set…
This paper aims to present objective methods for constructing new fuzzy sets from known fuzzy or classical sets, defined over the elements of a finite universe's superstructure. The paper proposes rules for assigning membership functions to…
Let k be a definable L-cardinal. Then there is a set of reals X, class-generic over L, such that L(X) and L have the same cardinals, X has size k in L(X) and some pi-1-2 formula defines X in all set-generic extensions of L(X). Two…
The forcing theorem is the most fundamental result about set forcing, stating that the forcing relation for any set forcing is definable and that the truth lemma holds, that is everything that holds in a generic extension is forced by a…