# Publications

Here is a list of my mathematical publications. I am only including the gzipped versions of the text files for download at this time. If you would like another format, feel free to email me at Dan.Talayco@gmail.com.
Abstracts are given below.**Applications of Cohomology to Set Theory I: Hausdorff Gaps**, *Annals of Pure and Applied Logic,* v. 71 (1995) pp. 69-106.**Applications of Cohomology to Set Theory II: Todorcevic Trees**, *Annals of Pure and Applied Logic,* v. 77 (1996) pp. 279-299.

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# Abstracts

## Abstract of *Applications I: *

We explore an application of homological algebra to set theoretic objects by developing a cohomology theory for Hausdorff gaps. This leads to a natural equivalence notion for gaps about which we answer questions by constructing many simultaneous gaps. The first result is proved in ZFC while new combinatorial hypotheses generalizing clubsuit are introduced to prove the second result. The cohomology theory is introduced with enough generality to be applicable to other questions in set theory.Additionally, the notion of an *incollapsible gap* is introduced and the existence of such a gap is shown to be independent of ZFC.

## Abstract of *Applications II: *

An application of homological algebra is explored by developing a cohomology theory for a class of Aronszajn trees. Properties of this class, called Todorcevic trees, are examined. The system is compared to that for Hausdorff gaps introduced previously and general results about both tree and gap systems are proven.