相关论文: Simple forcing notions and forcing axioms

The modal logic of forcing arises when one considers a model of set theory in the context of all its forcing extensions, interpreting necessity as "in all forcing extensions" and possibility as "in some forcing extension". In this modal…

Model semantics for first-order predicate logic is characterized by a visual inference tool called semantic forcing trees for predicate logic. Formulas that are valid (or invalid) by semantic forcing trees match valid (or invalid) formulas…

Let T be a countable, small simple theory. In this paper, we prove for such T, the notion of Lascar Strong type coincides with the notion of a strong type,over an arbitrary set.

The proofs first generated by automated theorem provers are far from optimal by any measure of simplicity. In this paper I describe a technique for simplifying automated proofs. Hopefully this discussion will stimulate interest in the…

The formalism proposed in Phys. Rev. Lett. 116, 078001 (2016) for determination of the normal and tangential inter-particle forces in frictional disks from visual data was criticized in a comment to that paper. However the theory developed…

This work formulates and gives grounds for general principles and theorems that question the energy function doctrine and its quantum version as a genuine law of nature without borders of adequacy. The emphasis is on the domain where the…

"Mathematicians, like physicists, are pushed by a strong fascination. Research in mathematics is hard, it is intellectually painful even if it is rewarding, and you would not do it without some strong urge." [D. Ruelle]. We shall give some…

In this article we adapt the existing account of class-forcing over a ZFC model to a model $(M,\mathcal{C})$ of Morse-Kelley class theory. We give a rigorous definition of class-forcing in such a model and show that the Definability Lemma…

In this paper we present an example of a simple study of velocity proportional resistance force. Some experimental determinations are presented.

We define the $\aleph_{1.5}$ chain condition. The corresponding forcing axiom is a generalization of Martin's Axiom and implies certain uniform failures of club--guessing on $\omega_1$ that don't seem to have been considered in the…

In this short note, we mimic the proof of the simplicity of the theory ACFA of generic difference fields in order to provide a criterion, valid for certain theories of pure fields and fields equipped with operators, which shows that a…

These are lecture notes from a course I gave at the University of Wisconsin during the Spring semester of 1993. Part 1 is concerned with Borel hierarchies. Section 13 contains an unpublished theorem of Fremlin concerning Borel hierarchies…

We discuss why AI is hard and why physics is simple. We discuss how physical intuition and the approach of theoretical physics can be brought to bear on the field of artificial intelligence and specifically machine learning. We suggest that…

We present a framework for model theoretic forcing in a non-first-order context, and present some applications of this framework to Banach space theory.

We introduce the notion of implicative algebra, a simple algebraic structure intended to factorize the model constructions underlying forcing and realizability (both in intuitionistic and classical logic). The salient feature of this…

We consider here Easton support iterations of Prikry type forcing notions. New ways of constructing normal ultrafilters in extensions are presented. It turns out that, in contrast with other supports, seemingly unrelated measures or…

In this paper we give a rigorous proof of the equivalence of some different forms of Faraday's law of induction clarifying some misconceptions on the subject and emphasizing that many derivations of this law appearing in textbooks and…

This is the second one in a series of papers classifying the factorizations of almost simple groups with nonsolvable factors. In this paper we deal with almost simple unitary groups.

We investigate the norms appearing in the forcing from combinatorial point of view. We make first steps towards building a catalog of the norms appearing in multiple settings and sources, reviewing four norms from Bartoszy\'nski and Judah…

We provide solutions to several problems of Foreman about ideals, several of which are closely related to Mitchell's notion of \emph{strongly proper} forcing. We prove: 1) Presaturation of a normal ideal implies projective antichain…