Related papers: Inaccessibility and Subinaccessibility. In two par…
We develop the theory of cofinal types of ultrafilters over measurable cardinals and establish its connections to Galvin's property. We generalize fundamental results from the countable to the uncountable, but often in surprisingly…
The property of countable metacompactness of a topological space gets its importance from Dowker's 1951 theorem that the product of a normal space X with the unit interval is again normal iff X is countably metacompact. In a recent paper,…
We prove a result concerning elementary embeddings of the set-theoretic universe into itself (Reinhardt embeddings) and functions on ordinals that "eventually dominate" such embeddings. We apply that result to show the existence of…
A system of singular integral equations with monotone and concave nonlinearity in the subcritical case is investigated. The specified system and its scalar analog have direct applications in various areas of physics and biology. In…
In this article we proved so-called strong reflection principles corresponding to formal theories Th which has omega-models. An posible generalization of the Lob's theorem is considered.Main results is: (1) let $k$ be an inaccessible…
This paper constructs a cirquent calculus system and proves its soundness and completeness with respect to the semantics of computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html). The logical vocabulary of the system consists of…
We show that the consistency of $\mathrm{ZF} + \mathrm{AD}_{\mathbb{R}} + ``\Theta$ is measurable$"$ implies the consistency of $\mathrm{ZF} +``\Theta$ is the least strongly regular cardinal and the least measurable cardinal$"$ + $``$all…
We deal with (< kappa)-supported iterated forcing notions which are (E_0,E_1)-complete, have in mind problems on Whitehead groups, uniformizations and the general problem. We deal mainly with the successor of a singular case. This continues…
We introduce the notion of $\mathcal{C}$-system of filters, generalizing the standard definitions of both extenders and towers of normal ideals. This provides a framework to develop the theory of extenders and towers in a more general and…
Inspired by Zermelo's quasi-categoricity result characterizing the models of second-order Zermelo-Fraenkel set theory $\text{ZFC}_2$, we investigate when those models are fully categorical, characterized by the addition to $\text{ZFC}_2$…
This paper deals with variety of problems in pcf theory and infinitary combinatorics. We look at normal filters and prc, measures of the size of [lambda]^{<kappa}, pcf-inaccessibility, entangled orders (and narrow Boolean Algebras),…
Let $\kappa$ be an inaccessible cardinal, $\mathfrak{U}$ be a universal algebra, and $\sim$ be the equivalence relation on $\mathfrak{U}^{\kappa}$ of eventual equality. From mild assumptions on $\kappa$ we give general constructions of…
Superstrong cardinals are never Laver indestructible. Similarly, almost huge cardinals, huge cardinals, superhuge cardinals, rank-into-rank cardinals, extendible cardinals, 1-extendible cardinals, 0-extendible cardinals, weakly superstrong…
Let $A$ be a finite-dimensional algebra over an algebraically closed field. The problem of constructing indecomposable $A$-modules inductively from simple ones by means of exact sequences - called accessibility - is the starting point of…
We generalise Jensen's result on the incompatibility of subcompactness with square. We show that alpha^+-subcompactness of some cardinal less than or equal to alpha precludes square_alpha, but also that square may be forced to hold…
In 1984, Ditor asked two questions: (1) For each $n\in\omega$ and infinite cardinal $\kappa$, is there a join-semilattice of breadth $n+1$ and cardinality $\kappa^{+n}$ whose principal ideals have cardinality $< \kappa$? (2) For each $n \in…
In [6] we proved that the universal theory of infinite free lattices is (algorithmically) decidable, leaving open the problem of decidability of the full theory of an (infinite) free lattice. We solve this problem by proving that, for every…
We introduce a new covering property, defined in terms of order types of sequences of open sets, rather than in terms of cardinalities of families. The most general form of this compactness notion depends on two ordinal parameters. In the…
We investigate categoricity of abstract elementary classes without any remnants of compactness (like non-definability of well ordering, existence of E.M. models or existence of large cardinals). We prove (assuming a weak version of GCH…
Contents: 1. Introduction. 2. The Early Years. 2.1 Living Without Field Theory. 2.2 Initial Postulates. 2.3 Further Postulates. 2.4 QCD and a Final Postulate. 2.5 Analyticity in Field Theory. 3. Axiomatic S-Matrix Theory. 3.1 Unitarity,…