223 citations · 725 across the 95 of their papers we have counts for
5 papers · 1 filter
Upward closure and amalgamation in the generic multiverse of a countable model of set theory
Joel David Hamkins
I prove several theorems concerning upward closure and amalgamation in the generic multiverse of a countable transitive model of set theory. Every such model has forcing extens…
A position in infinite chess with game value
C. D. A. Evans, Joel David Hamkins, Norman Lewis Perlmutter
We present a position in infinite chess exhibiting an ordinal game value of , thereby improving on the previously largest-known values of and .
Open determinacy for class games
Victoria Gitman, Joel David Hamkins
The principle of open determinacy for class games---two-player games of perfect information with plays of length , where the moves are chosen from a possibly proper class, such…
Ehrenfeucht's lemma in set theory
Gunter Fuchs, Victoria Gitman, Joel David Hamkins
Ehrenfeucht's lemma (1973) asserts that whenever one element of a model of Peano arithmetic is definable from another, then they satisfy different types. We consider here the analo…
Incomparable -like models of set theory
Gunter Fuchs, Victoria Gitman, Joel David Hamkins
We show that the analogues of the Hamkins embedding theorems, proved for the countable models of set theory, do not hold when extended to the uncountable realm of -like models…