bio | website | jvanname.myweb.usf.edu |
---|---|---|
location | Gotham, NY | |
age | 25 | |
visits | member for | 3 years, 5 months |
seen | 42 mins ago | |
stats | profile views | 3,589 |
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 |