Characterisations of variant transfinite computational models: Infinite time Turing, ordinal time Turing, and Blum–Shub–Smale machines

Autor: Philip D. Welch

Publikováno v: Computability. 10:159-180

We consider how changes in transfinite machine architecture can sometimes alter substantially their capabilities. We approach the subject by answering three open problems touching on: firstly differing halting time considerations for machines with mu

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::a81eba29ef0a57084bb1aa79f691e08f
https://doi.org/10.3233/com-200301

GAMES AND RAMSEY-LIKE CARDINALS

Autor: Dan Saattrup Nielsen, Philip D. Welch

Publikováno v: Nielsen, D S & Welch, P 2019, ' Games and ramsey-like cardinals ', Journal of Symbolic Logic, vol. 84, no. 1, pp. 408-437 . https://doi.org/10.1017/jsl.2018.75

We generalise the $\alpha$-Ramsey cardinals introduced in Holy and Schlicht (2018) for cardinals $\alpha$ to arbitrary ordinals $\alpha$, and answer several questions posed in that paper. In particular, we show that $\alpha$-Ramseys are downwards abs

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5f943c559b6e2be063317547d4940dd5
https://doi.org/10.1017/jsl.2018.75

Lower consistency bounds for mutual stationarity with divergent uncountable cofinalities

Autor: Dominik Adolf, Sean Cox, Philip D. Welch

Publikováno v: Adolf, D, Cox, S & Welch, P D 2018, ' Lower consistency bounds for mutual stationarity with divergent uncountable cofinalities ', Israel Journal of Mathematics, vol. 228, no. 1, pp. 1-19 . https://doi.org/10.1007/s11856-018-1771-4

We prove that the upper bounds for the consistency strength of certain instances of mutual stationarity considered by Liu-Shelah~\cite{MR1469093} are close to optimal. We also consider some related and, as it turns out, stronger properties.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::70ee27eb9fda0b8570056e2a8977ac6f
https://doi.org/10.1007/s11856-018-1771-4

Obtaining Woodin’s cardinals

Autor: Philip D. Welch

Publikováno v: Welch, P D 2017, Obtaining Woodin's cardinals . in A E Caicedo, J Cummings, P Koellner & P B Larson (eds), Foundations of Mathematics : Logic at Harvard: Essays in Honor of W. Hugh Woodin's 60th Birthday, March 27-29 2015, Harvard University, Cambridge, MA . Contemporary Mathematics, vol. 690, American Mathematical Society, pp. 161-176 . https://doi.org/10.1090/conm/690/13867

Since the 1980’s work on Projective Determinacy and AD the concept of Woodin cardinal has become to be seen as central in the theory of large cardinals and inner model theory. The use by Woodin himself of a background assumption in many arguments t

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::95c5e4fea7fb548fa2e918f6108c935b
https://doi.org/10.1090/conm/690/13867

Proving Theorems from Reflection

Autor: Philip D. Welch

Publikováno v: Synthese Library ISBN: 9783030156541
Welch, P D 2019, Proving Theorems from Reflection . in S Centron, D Sarikaya & D Kant (eds), Reflections on the Foundations of Mathematics : Univalent Foundations, Set Theory and General Thoughts . Synthese Library in Philosophy, vol. 407, Springer, Cham, pp. 79-97 . https://doi.org/10.1007/978-3-030-15655-8_4

We review some fundamental questions concerning the real line of mathematical analysis, which, like the Continuum Hypothesis, are also independent of the axioms of set theory, but are of a less ‘problematic’ nature, as they can be solved by adopt

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::95b87c6e59943dd5e58ba36a3d229ca3
https://doi.org/10.1007/978-3-030-15655-8_4