“Filters on Posets and Generalizations” – updated
Filters on Posets and Generalizations online article updated as an accomplishment of this plan. This is important primarily to extend the category of pointfree funcoids with objects being arbitrary posets (even without least element). That way this category would become more “complete”. To extend that is required a definition of intersecting elements of a poset […]
Generalization in ZF
I wrote short article “Generalization in ZF” accompanied with Isabelle/ZF sources. This is a draft and alpha. I await your comments on both the article and Isabelle sources. I’m sure my Isabelle sources may be substantially improved (and I plan to work over this). Comments are welcome. After hearing your comments and improving the files, […]
A little error corrected
I corrected a small error in “Filters on Posets and Generalizations” article. The error was in Appendix B in the proof of the theorem stating $latex (t;x)\not\in S$ (I messed $latex t$ and $latex \{t\}$.)
I take a vacation in my research work
I decided to dedicate my free (of working as a programmer) time to write a book about religion (What book? It will be a surprise.) So in a few nearby months I am going to not continue my math research. I am going to return to math research after I will finish that religious book. […]
Strong vs weak partitioning – counterexample
My problem whether weak partitioning and strong partitioning of a complete lattice are the same was solved by counter-example by François G. Dorais. Remains open whether strong and weak partitioning of a filter object is the same.
Principal filters are center – solved
I have proved this conjecture: Theorem 1 If $latex {\mathfrak{F}}&fg=000000$ is the set of filter objects on a set $latex {U}&fg=000000$ then $latex {U}&fg=000000$ is the center of the lattice $latex {\mathfrak{F}}&fg=000000$. (Or equivalently: The set of principal filters on a set $latex {U}&fg=000000$ is the center of the lattice of all filters on $latex […]
Formalistics of generalization
In the framework of ZF formally considered generalizations, such as whole numbers generalizing natural number, rational numbers generalizing whole numbers, real numbers generalizing rational numbers, complex numbers generalizing real numbers, etc. The formal consideration of this may be especially useful for computer proof assistants.
My new math blog
I abandoned my old blogs at my own site and moved to WordPress.com. This is my new math blog. Here I will tell about my math research.