相关论文: Simple forcing notions and forcing axioms

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…

In this paper, we study (zero) forcing sets which induce connected subgraphs of a graph. The minimum cardinality of such a set is called the connected forcing number of the graph. We provide sharp upper and lower bounds on the connected…

The landmark Levy-Solovay Theorem limits the kind of large cardinal embeddings that can exist in a small forcing extension. Here I announce a generalization of this theorem to a broad new class of forcing notions. One consequence is that…

Let I be a sigma-ideal sigma-generated by a projective collection of closed sets. The forcing with I-positive Borel sets is proper and adds a single real r of an almost minimal degree: if s is a real in V[r] then s is Cohen generic over V…

There are three goals of this thesis. First: to present a concise yet accessible description of basic mathematical logic and model theory. Second: to develop an axiomatization of special relativity using only two undefined predicates.…

Which mechanisms are simple to play? When is it easy for participants to see that a mechanism is incentive-compatible? I will start by explaining how and why economists came to ask these questions. Then I will discuss three recent answers,…

In this paper we prove that the maximum principle in forcing is equivalent to the axiom of choice. The maximum principle is the property of forcing: p ||- exists x theta(x) iff for some name tau p ||- theta(tau). We also look at three…

We develop librationism, {\pounds}, and clarify some mathematical and philosophical matters which relate to the particular manner in which it deals with the paradoxes and to its usefulness as a foundation for mathematics and type free…

Estimating the expected impact of an article is valuable for various applications (e.g., article/cooperator recommendation). Most existing approaches attempt to predict the exact number of citations each article will receive in the near…

We present a notion of forcing that can be used, in conjunction with other results, to show that there is a Martin-L\"of random set X such that X does not compute 0' and X computes every K-trivial set.

We describe a method of building ``nice'' sigma-ideals from Souslin ccc forcing notions. [These notes were written down in 1992, but were not submitted to any journal. In a slightly modified form, they were incorporated to: T. Bartoszynski…

We give a forcing construction of the square principle on omega_1 using forcing with conditions whose domain is finite.

The purpose of this paper is to outline a simple set of axioms for basic set theory from which most fundamental facts can be derived. The key to the whole project is a new axiom of set theory which I dubbed "The Law of Extremes". It allows…

This paper presents a type theory with a form of equality reflection: provable equalities can be used to coerce the type of a term. Coercions and other annotations, including implicit arguments, are dropped during reduction of terms. We…

We propose analyzing conditional reasoning by appeal to a notion of intervention on a simulation program, formalizing and subsuming a number of approaches to conditional thinking in the recent AI literature. Our main results include a…

A simple definition of torsion theory is presented, as a factorization system with both classes satisfying the 3--for--2 property. Comparisons with the traditional notion are given, as well as connections with the notions of fibration and…

We apply a general approach for distributions of binary isolating and semi-isolating formulas to the class of strongly minimal theories.

Fairness-aware learning aims at satisfying various fairness constraints in addition to the usual performance criteria via data-driven machine learning techniques. Most of the research in fairness-aware learning employs the setting of…

We present a method to simplify expressions in the context of an equational theory. The basic ideas and concepts of the method have been presented previously elsewhere but here we tackle the difficult task of making it efficient in…

We introduce a generalized notion of inference system to support more flexible interpretations of recursive definitions. Besides axioms and inference rules with the usual meaning, we allow also coaxioms, which are, intuitively, axioms which…