Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 5 of 5 for “"large cardinals"”.
-
Aspects of Large Cardinals (Set Theory, Logic, Measurable, Strongly Compact, Extendible)
… a categorical representation of measurable cardinals. The result answers Girard's presumption "The solution to make the order relation between dilators total will be connected to large cardinal axioms, if it exists" negatively. As a byproduct, we obtain the following interesting result …
-
The dichotomy in the determinacy of certain two-person infinite games with moves from {0,1}
… {0,1} is true regardless of the existence of large cardinals for n ≥ 2. We show that this is not true, however, for some more complex games: For k ≥ 3 and n ≥ 2, the determinacy of P0k games with length o·n and with moves from {0,1} is equivalent to the determinacy of P0k games with length …
-
The search for new axioms
… reflection principle (known to be consistent via large cardinals) can overcome the minimal hurdle and yield a significant reduction in incompleteness. In Chapter 4 I introduce a new approach to justifying new axioms-extension principles-and show that such principles can overcome the minimal hurdle …
-
Sigma_n-correct Forcing Axioms
… axioms are consistent relative to a hierarchy of large cardinals generalizing supercompactness and extendibility whose supremum is the first-order version of Vopenka's Principle.</p> <p>By analogy to classical forcing axioms, there is also a hierarchy of Sigma_n-correct bounded forcing axioms …
-
Axiomatization and Incompleteness in Arithmetic and Set Theory
… reduction in incompleteness can be effected by large cardinal axioms justified using extrinsic methods analogous to the principles of theory choice in natural science. This undercuts the traditional justification for many large cardinal axioms, so I end with a sketch of how conceptual platonism …