Zobrazeno 1 - 10
of 340
pro vyhledávání: '"HAMKINS, JOEL DAVID"'
Autor:
Hamkins, Joel David
I describe a simple historical thought experiment showing how we might have come to view the continuum hypothesis as a fundamental axiom, one necessary for mathematics, indispensable even for calculus.
Comment: 19 pages. Commentary can be made o
Comment: 19 pages. Commentary can be made o
Externí odkaz:
http://arxiv.org/abs/2407.02463
Autor:
Hamkins, Joel David, Nenu, Theodor
We discuss the accuracy of the attribution commonly given to Turing's 1936 paper "On computable numbers..." for the computable undecidability of the halting problem, coming eventually to a nuanced conclusion.
Comment: 18 pages. Commentary may be
Comment: 18 pages. Commentary may be
Externí odkaz:
http://arxiv.org/abs/2407.00680
Autor:
Hamkins, Joel David
Every mathematical structure has an elementary extension to a pseudo-countable structure, one that is seen as countable inside a suitable class model of set theory, even though it may actually be uncountable. This observation, proved easily with the
Externí odkaz:
http://arxiv.org/abs/2210.04838
Autor:
Hamkins, Joel David
According to the math tea argument, there must be real numbers that we cannot describe or define, because there are uncountably many real numbers, but only countably many definitions. And yet, the existence of pointwise-definable models of set theory
Externí odkaz:
http://arxiv.org/abs/2209.12578
Autor:
Hamkins, Joel David
The standard treatment of sets and definable classes in first-order Zermelo-Fraenkel set theory accords in many respects with the Fregean foundational framework, such as the distinction between objects and concepts. Nevertheless, in set theory we may
Externí odkaz:
http://arxiv.org/abs/2209.07845
Autor:
Hamkins, Joel David
Many set theorists point to the linearity phenomenon in the hierarchy of consistency strength, by which natural theories tend to be linearly ordered and indeed well ordered by consistency strength. Why should it be linear? In this paper I present cou
Externí odkaz:
http://arxiv.org/abs/2208.07445
Reflection in second-order set theory with abundant urelements bi-interprets a supercompact cardinal
Autor:
Hamkins, Joel David, Yao, Bokai
After reviewing various natural bi-interpretations in urelement set theory, including second-order set theories with urelements, we explore the strength of second-order reflection in these contexts. Ultimately, we prove, second-order reflection with
Externí odkaz:
http://arxiv.org/abs/2204.09766
Autor:
Hamkins, Joel David
I consider the natural infinitary variations of the games Wordle and Mastermind, as well as their game-theoretic variations Absurdle and Madstermind, considering these games with infinitely long words and infinite color sequences and allowing transfi
Externí odkaz:
http://arxiv.org/abs/2203.06804
Autor:
Hamkins, Joel David, Leonessi, Davide
We introduce the game of infinite Hex, extending the familiar finite game to natural play on the infinite hexagonal lattice. Whereas the finite game is a win for the first player, we prove in contrast that infinite Hex is a draw -- both players have
Externí odkaz:
http://arxiv.org/abs/2201.06475
Autor:
Hamkins, Joel David, Leonessi, Davide
Infinite draughts, or checkers, is played just like the finite game, but on an infinite checkerboard extending without bound in all four directions. We prove that every countable ordinal arises as the game value of a position in infinite draughts. Th
Externí odkaz:
http://arxiv.org/abs/2111.02053