Mathematical
Logic Papers
TopoLogic
TopoLogic | Generalized Equivalence
"Monadic
characterizations in nonstandard topology," Zeitschrift
fur Mathematische Logik und Grundlagen der Mathematik 26
(1980) 395-397.
"Quantification
of Greek variables in calculus," Mathematics Magazine
50 (1977) 27-29.
These
papers show why epsilons and deltas tend to get quantified in
particular ways in calculus, and how some of these same ideas
appear in nonstandard topology.
"Sentences
preserved between equivalent topological bases," Zeitschrift
fur Mathematische Logik und Grundlagen der Mathematik 22
(1976) 79-84.
"Infinitary
logic and topological homeomorphisms," Zeitschrift fur Mathematische
Logik und Grundlagen der Mathematik 21
(1975) 405-408.
These
two papers introduced a practical two-sorted infinitary language
for topology. The following places this in a broader setting:
J.
Flum and M. Ziegler, Topological Model Theory, Lecture
Notes in Mathematics #769, Springer (1990).
Generalized
Equivalence
TopoLogic | Generalized Equivalence
"Generalized
equivalence and the foundations of quasigroups," Notre Dame
Journal of Formal Logic 21 (1980) 135-140.
"Generalized
equivalence and the phraseology of configuration theorems," Notre
Dame Journal of Formal Logic 21 (1980)
141-147.
These
two papers use generalized equivalence to discuss certain nuts
and bolts in the combinatorial structures of quasigroups and
finite geometries.
"Generalized
equivalence: A pattern of mathematical expression," Studia
Logica 44 (1985) 295-289.
This
looks at the common phenomena in mathematics of having three
statements, every two of which implies the third (or any number
of statements with the truth of all but an arbitrary one always
implying them all; traditional "equivalence" is the special
case with just two statements). A broad sample of examples is
given.
TopoLogic | Generalized
Equivalence
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