We introduce a new simple first-order framework for theories whose objects are wellorderings (lists). A system ALT (axiomatic list theory) is presented and shown to be equiconsistent with ZFC (Zermelo Fraenkel Set Theory with the Axiom of Choice). The theory sheds new light on the power set axiom and on Gödel’s axiom of constructibility. In list theory there are strong arguments favoring Gödel’...

The language for the formulation of the interesting statements is, of course, most important. We use first order predicate logic. Our main achievement in this paper is an axiom system which we believe to be more powerful than any other natural general purpose discovery axiom system. We prove soundness of this axiom system in this paper. Additionally we prove that if we remove some of the requir...

If T is a complete theory stronger than ZFFin such that axiom of extensionality for classes + T + (9X) i is consistent for 1 i k (each alone), where i are normal formulae then we showAST + (9X) 1+ +(9X) k + scheme of choice is consistent. As a consequence we get: there is no proper 1-formula inAST + scheme of choice. Moreover the complexity of the axioms of AST is studied, e.g. we show axiom of...

In this article, we provide the epistemicentrenchment characterization of the weak version of Parikh’s relevance-sensitive axiom for belief revision — known as axiom (P) — for the general case of incomplete theories. Loosely speaking, axiom (P) states that, if a belief set K can be divided into two disjoint compartments, and the new information φ relates only to the first compartment, then the ...

We introduce ‘subgroup additivity’ as our main axiom and investigate its implications for the queueing problem. The axiom of subgroup additivity requires that a rule assigns the same expected ‘relative’ utility to each agent whether an agent’s expected relative utility is calculated from the problem involving all agents or from its sub-problems with a smaller number of agents. As a result, we p...

Quality control is an essential task within ontology development projects especially when the knowledge formalization is partially automatized. In this paper, we propose a reasoning-based, interactive approach to support the revision of formalized knowledge. We state consistency criteria for revision states and introduce the notion of revision closure, based on which the revision of ontologies ...

For Axiom A diffeomorphisms and equilibrium states, we prove a Large deviations result for the sequence of successive return times into a fixed Borel set, under some assumption on the boundary. Our result relies on and extends the work by Chazottes and Leplaideur who considered cylinder sets of a Markov partition.

We introduce a new reflection principle which we call “Fodor-type Reflection Principle” (FRP). This principle follows from but is strictly weaker than Fleissner’s Axiom R. For instance, FRP does not impose any restriction on the size of the continuum, while Axiom R implies that the continuum has size ≤ א2. We show that FRP implies that every locally separable countably tight topological space X...

Verjovsky stated the conjecture in [35] for all dimensions with an additional assumption that the fundamental group of the manifold is solvable. This was proved by Plante [24, 25] and Armendariz [4], who showed that the conjecture is true if and only if the fundamental group of the manifold is solvable. In the above form, the conjecture first appeared in Ghys [13]. However, Ghys has pointed out...

This paper is an introduction to forcing axioms and large cardinals. Specifically, we shall discuss the large cardinal strength of forcing axioms in the presence of regularity properties for projective sets of reals. The new result shown in this paper says that ZFC + the bounded proper forcing axiom (BPFA) + “every projective set of reals is Lebesgue measurable” is equiconsistent with ZFC + “th...