11,017 reputation
12644
bio website jvanname.myweb.usf.edu
location Gotham, NY
age 25
visits member for 3 years, 5 months
seen 42 mins ago

I am interested in to varying degrees ordered sets, general topology, point-free topology, Boolean algebras, set-theory, universal algebra, and model theory. Most of my previous mathematics research involves dualities that are similar to Stone duality. I am currently interested in using forcing extensions to study objects such as Boolean algebras and frames in the ground model. Furthermore, I am also interested in self-distributive algebras with operations of arbitrary finite arity and their relations with algebras of rank-into-rank elemetary embeddings and other mathematical structures.


Aug
25
comment How big is the lattice of all functions?
Several cardinal invariants of this lattice are the well-known cardinal characteristics of the continuum such as bounding number or the dominating number. The cardinal characteristics of the continuum are described in detail by Andreas Blass in chapter 6 in the Handbook of Set Theory.
Aug
20
comment Quotients of powers of the Sierpinski space
Any quotient of a power of a Sierpinski space must be quasicompact.
Aug
18
accepted Is the variety of algebras $(A,*,+)$ that satisfy $(x*y)+(y*z)=(x+y)*(y+z)$ generated by its finite algebras?
Aug
18
accepted Does there exist an uncountable partition of a Polish space so that the union of any collection of blocks is Borel?
Aug
18
asked Does there exist an uncountable partition of a Polish space so that the union of any collection of blocks is Borel?
Aug
17
revised Is it possible for a separable metric and a non-separable metric to have the same Borel $\sigma$-algebra?
Added information answering other question.
Aug
17
asked Is the variety of algebras $(A,*,+)$ that satisfy $(x*y)+(y*z)=(x+y)*(y+z)$ generated by its finite algebras?
Aug
14
comment Surjectively rigid partially ordered sets
Joel David Hamkins. I forgot to mention that the mappings $f$ and $g$ are not the identity mapping. I edited the answer to cover this case.
Aug
14
revised Surjectively rigid partially ordered sets
added 230 characters in body
Aug
14
answered Surjectively rigid partially ordered sets
Aug
13
answered Does every set $X$ have a topology for which the only continuous self-surjection is the identity map?
Aug
12
answered In which sense “closure” is a closure?
Aug
10
answered Is it possible for a separable metric and a non-separable metric to have the same Borel $\sigma$-algebra?
Aug
10
awarded  Inquisitive
Aug
9
comment How distributive are the bad Laver tables?
I am familiar with most of the literature on the distributive Laver tables, but there does not appear to be much literature on the "bad" (non-distributive) Laver tables since they do not appear to have much use besides being a construction that includes the distributive Laver tables $S_{2^{n}}$.
Aug
9
comment How distributive are the bad Laver tables?
If $m,n$ are integers, then the mapping $\phi:S_{2^{n}\cdot m}\rightarrow S_{2^{n}}$ where $\phi(x)=x\,\text{mod}\, 2^{n}$ is a homomorphism, so the algebra $S_{n}$ is not simple whenever $n$ is even. The algebras $S_{n}$ are have no nontrivial automorphisms since $1$ is the unique generator for each of the algebras $S_{n}$. There are many ways to embed Laver tables $S_{2^{n}}$ into larger Laver tables $S_{2^{m}}$ (Drapal has proven some results about embedding smaller Laver tables into larger Laver tables).
Aug
9
asked How distributive are the bad Laver tables?
Aug
9
answered Is there a name for a partial order in which there is a countable chain which “dominates” the whole space?
Aug
7
awarded  Necromancer
Jul
28
answered Baire Category Theorem for complete uniform spaces