4 papers
Closed Unbounded classes and the Haertig Quantifier Model
Philip Welch
We show that assuming modest large cardinals, there is a definable class of ordinals, closed and unbounded beneath every uncountable cardinal, so that for any closed and unbounded…
Stably Measurable Cardinals
P. D. Welch
We define a weak iterability notion that is sufficient for a number of arguments concerning -definability at uncountable regular cardinals. In particular we give its exact con…
Lower consistency bounds for mutual stationarity with divergent uncountable cofinalities
Dominik Adolf, Sean Cox, Philip Welch
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 cons…
Discrete Transfinite Computation
Philip Welch
We describe various computational models based initially, but not exclusively, on that of the Turing machine, that are generalized to allow for transfinitely many computational ste…