Let T̄ 3 s be arbitrary. Every student is aware that every field is Artinian and injective. We show that Erdős’s conjecture is true in the context of Eisenstein manifolds. We wish to extend the results of [19] to homeomorphisms. Hence in future work, we plan to address questions of maximality as well as invertibility.

Abstract This paper investigates the semantics of an understudied Mandarin numeral construction type, here dubbed da -NumPs (i.e. number word < ‘big’ noun). Drawing primarily upon evidence from online corpora, we argue for a taxonomy this that comprises two distinct interpretations, based on scalarity morpheme and its composition with other constituents within construction. Specifically, one...

Hamkins and Kikuchi (2016, 2017) show that in both set theory class the definable subset ordering of universe interprets a complete decidable theory. This paper identifies minimum subsystem ZF $\mathsf {ZF}$ , BAS {BAS}$ ensures theory, classifies structures can be realised as relation model this Extending refining Kikuchi's result for extension, IABA Ideal {IABA}_{\mathsf {Ideal}}$ infinite at...

Infinite time register machines (ITRMs) are register machines which act on natural numbers and which are allowed to run for arbitrarily many ordinal steps. Successor steps are determined by standard register machine commands. At limit times a register content is defined as a lim inf of previous register contents, if that limit is finite; otherwise the register is reset to 0. (A previous weaker ...

The principal result of this paper answers a long-standing question in the model theory of arithmetic [KS, Question 7] by showing that there exists an uncountable arithmetically closed family A of subsets of the set ω of natural numbers such that the expansion ΩA := (ω, +, ·, X)X∈A of the standard model of Peano arithmetic has no conservative elementary extension, i.e., for any elementary exten...

In this thesis, we investigate the modal logic of forcing and the modal logic of grounds of generic multiverses. Hamkins and Löwe showed that the ZFC-provable modal principles of forcing, as well as of grounds, are exactly the theorems of the modal logic S4.2 (see [16],[17]). We prove that the modal logic of forcing of any generic multiverse is also exactly S4.2 by showing that any model of ZFC...

I will discuss a new class of forcing axioms, the Resurrection Axioms (RA), and the Weak Resurrection Axioms (wRA). While Cohen’s method of forcing has been designed to change truths about the set-theoretic universe you live in, the point of Resurrection is that some truths that have been changed by forcing can in fact be resurrected, i.e. forced to hold again. In this talk, I will illustrate h...

We introduce the unifying notion of delimiting diagram. Hitherto unrelated results such as: Minimality of the internal needed strategy for orthogonal first-order term rewriting systems, maximality of the limit strategy for orthogonal higher-order pattern rewrite systems (with maximality of the strategy F∞ for the λ-calculus as a special case), and uniform normalisation of balanced weak Church–R...