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Abstract: In this thesis, we develop four systems of set theory based on linear logic. All of those systems have the principle of unrestricted comprehension but they are shown to be consistent. The consitency proofs are given by establishing the cut-elimination theorems. Our first system of linear set theory SMALL is formulated in full linear logic, i.e., with exponentials. However we do not allow exponentials to appear inside of set terms. Secondly, we formulate a system of set theory in linear logic... (Update)
Context of citations to this paper: More
.... studied for the reason that the use of unrestricted comprehension does not necessarily yield the contradiction in such logics [2, 4, 6, 7, 9]. However, it has been also noticed that the standard extetensionality axiom cannot be added to such a set theory without causing...
...result. cut elimination is not preserved when the exponentials interact with set comprehension; this situation is investigated in [Shi94]. This note is structured as follows. First we recall FILL and discuss a few examples. In the next section we attack the problem of...
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BibTeX entry: (Update)
M. Shirahata. Linear Set Theory. Dissertation, Department of Philosophy, Stanford University, 1994. http://citeseer.ist.psu.edu/shirahata95linear.html More
@phdthesis{ shirahata94linear,
author = "Masaru Shirahata",
title = "Linear Set Theory",
year = "1994",
url = "citeseer.ist.psu.edu/shirahata95linear.html" }
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