Related papers: The seed order
In this paper I will show that it is relatively consistent with the usual axioms of mathematics (ZFC) together with a strong form of the axiom of infinity (the existence of a supercompact cardinal) that the class of uncountable linear…
An ultraproduct can be a helpful organizing principle in presenting solutions of problems at many levels, as argued by Terence Tao. We apply it here to the solution of a calculus problem: every infinite sequence has a monotone infinite…
We extend some of our earlier results on the interconnection between ultrafilter extensions, and ultrapowers. Throughout we restrict ourselves to relational structures with one binary relation. Recently it was shown that for bounded…
We characterize sums of normal ultrafilters after the Magidor iteration (product) of Prikry forcings over a discrete set of measurable cardinals. We apply this to show that the weak Ultrapower Axiom is not equivalent to the Ultrapower…
We consider a family of distributions on which natural tail orders can be constructed upon a representation of a distribution by a (single) hyper-real number. Past research revealed that the ordering can herein strongly depend on the…
An infinite cardinal $\lambda$ is called Fr\'echet if the Fr\'echet filter on $\lambda$ extends to a countably complete ultrafilter. We investigate the relationship between Fr\'echet cardinals and strongly compact cardinals under a…
We define what is meant by a strict total order in a category having subobjects, products and fibre products. This allows us to define the notions of an ordered bundle X and an ordered G-set; when G=\pi_1(X) we relate these structures to…
We consider methods for aggregating preferences that are based on the resolution of discrete optimization problems. The preferences are represented by arbitrary binary relations (possibly weighted) or incomplete paired comparison matrices.…
Social welfare orders seek to combine the disparate preferences of an infinite sequence of generations into a single, societal preference order in some reasonably-equitable way. In [2] Dubey and Laguzzi study a type of social welfare order…
Well-quasi orders such as homeomorphic embedding are commonly used to ensure termination of program analysis and program transformation, in particular supercompilation. We compare eight well-quasi orders on how discriminative they are and…
The logic L^1_\theta introduced in [Sh:797]; it is the maximal logic below L_theta theta in which a well ordering is not definable. We investigate it for theta a compact cardinal. We prove it satisfies several parallel of classical theorems…
We continue the research of an extension $\widetilde{\mid}$ of the divisibility relation to the Stone-\v Cech compactification $\beta N$. First we prove that ultrafilters we call prime actually possess the algebraic property of primality.…
Algorithmic decidability is established for two order-theoretic properties of downward closed subsets defined by finitely many obstructions in two infinite posets. The properties under consideration are: (a) being atomic, i.e. not being…
We are interested in generalizing part of the theory of ultrafilters on omega to larger cardinals. Here we set the scene for further investigations introducing properties of ultrafilters in strong sense dual to being normal.
In the first edition of Classification Theory, the second author characterized the stable theories in terms of saturation of ultrapowers. Prior to this theorem, stability had already been defined in terms of counting types, and the unstable…
This short note contains the proofs of two small but somewhat surprising results about ultrafilters on $\mathbb{N}$: 1. strongly summable ultrafilters are rapid, 2. every rapid ultrafilter induces a closed left ideal of rapid ultrafilters.…
Higher-order unification has been shown to be undecidable. Miller discovered the pattern fragment and subsequently showed that higher-order pattern unification is decidable and has most general unifiers. We extend the algorithm to…
We motivate and study an infinite sequence of binary operations on the ordinal numbers, extending the standard arithmetic on the ordinals to higher degrees of iteration. Connections to the hyperoperations on the natural numbers are…
A variety of classes of naturally arising ultrafilters on omega is discussed, and the question is raised whether it is consistent that the classes are empty. Since all the classes contain the P-point ultrafilters, a negative answer would…
For a free ultrafilter U on omega we study several cardinal characteristics which describe part of the combinatorial structure of U. We provide various consistency results; e.g. we show how to force simultaneously many characters and many…