In this blog post I will travel back to the 70s and discuss about a result that appeared in (Menas, 1974). Briefly, the result says that we can always find f...
Welcome to my personal webpage!
I am a PhD graduate from the University of Bristol working in set theory, an area of mathematical logic. Most of my research has to do with the interaction between large cardinals and forcing, as a means to explore the limitations of the standard axiomatic system ZFC or to find the consistency strength of various mathematical statements.
Lately, I have become interested in the concept of strong compactness, one of the most natural, yet pathological, large cardinal notions. Strongly compact cardinals have a strong impact on the combinatorial properties of larger cardinals and there is ongoing research to understand its full extent. However, unlike other large cardinals they suffer from the so called "identity crisis", which means that a strongly compact cardinal can be very small or very large, depending on the model of ZFC we choose to work in.
In my thesis I devised a new large cardinal notion, obtained by "Woodinising" strongly compact cardinals. Although this notion is a very powerful form of strong compactness, it still inherits the identity crisis feature of strongly compact cardinals. However, it is a reasonable large cardinal notion, as it resembles the well-known notions of Woodin and Vopěnka cardinals.
I wish to continue my research on the concept of strong compactness and study its connections with combinatorics and topology.
Time for the first ever blog post! And it is about one of my favourite topics, the preservation of large cardinals through forcing.
Woodin and Vopěnka cardinals are established notions in the large cardinal hierarchy and it is known that Vopenka cardinals are the Woodin analogue for super...
Results about Woodin cardinals and forcing.