Search
Search Results
-
The second-order version of Morley’s theorem on the number of countable models does not require large cardinals
The consistency of a second-order version of Morley’s Theorem on the number of countable models was proved in [EHMT23] with the aid of large...
-
Perfect subtree property for weakly compact cardinals
We investigate the consistency strength of the statement: κ is weakly compact and there is no tree on κ with exactly κ + many branches. We show that...
-
Forcing level by level equivalence and a consequence of UA
We show how Hamkins’ Gap Forcing Theorem of Hamkins (Israel J Math 125:237–252, 2001, Bull Symb Logic 5: 264–272, 1999) can be used to give an...
-
Reflection Principles, Generic Large Cardinals, and the Continuum Problem
Strong reflection principles with the reflection cardinal \(\le \aleph _1\)...
-
Critical cardinals
We introduce the notion of a critical cardinal as the critical point of sufficiently strong elementary embedding between transitive sets. Assuming...
-
Cohomological Localizations and Set-Theoretical Reflection
Homological localizations of spaces and spectra have been a fundamental tool in algebraic topology since the 1970s, especially in the setting of...
-
Model theoretic characterizations of large cardinals
We consider compactness characterizations of large cardinals. Based on results of Benda [Ben78], we study compactness for omitting types in various...
-
On κ-compact cardinals
We deal with some questions related to κ -compact cardinals.
-
A Galvin–Hajnal theorem for generalized cardinal characteristics
We prove that a variety of generalized cardinal characteristics, including meeting numbers, the rea** number, and the dominating number, satisfy an...
-
On Supercompactness of \(\omega _1\)
This paper studies structural consequences of supercompactness of \(\omega _1\)...
-
A small ultrafilter number at smaller cardinals
It is proved to be consistent relative to a measurable cardinal that there is a uniform ultrafilter on the real numbers which is generated by fewer...
-
Mathematical Practices Can Be Metaphysically Laden
In this chapter I explore the reciprocal relationship between the metaphysical views mathematicians hold and their mathematical activity. I focus on...
-
Combinatorial properties and dependent choice in symmetric extensions based on Lévy collapse
We work with symmetric extensions based on Lévy collapse and extend a few results of Apter, Cody, and Koepke. We prove a conjecture of Dimitriou from...
-
Reflection principles, GCH and the uniformization properties
Reflection principles (or dually speaking, compactness principles) often give rise to combinatorial guessing principles. Uniformization properties,...