My research interests are set theory, logic, discrete math and the connections between these areas. A list of my published work follows (many are downloadable in pdf form). I am also very interested in using Mathematica to get students to discover mathematics. I taught a course at Queens in our Mathematics Laboratory which teaches Mathematica through a series of mathematical problems and have written a Lab Manual, with John Kennedy, called "Discovering Mathematics with Mathematica(available here). I am now retired but still actively engaged in research.
- 1965. An elementary fixed point theorem, Amer. Math. Monthly 72, 165- 67.pdf
- 1970. A new proof of the compactness theorem for propositional logic, Notre Dame J. Formal Logic 11, 79-80. pdf
- 1971. Superinductive classes in class-set theory, Notre Dame J. Formal Logic 12, 62-68. pdf file
- 1972. A short proof of Rado's lemma, J. Combinatorial Theory 12, 299-300. pdf
- 1973. Some combinatorial theorems equivalent to the prime ideal theorem, Proc. Amer. Math. Soc. 41, 268-273. pdf
- 1975. A characterization of logical consequence in
quantification theory, Notre Dame J. Formal Logic 3, 375-377. pdf
- 1976. A simple proof of the reflection property for parabolas, Two-year College Math. J. 7, 59-60.
- 1976. Elementary equivalence and constructible models of ZF, Zeit. f. Math. Logik 22, 333-338.
- 1977. Generalizing Konig's infinity lemma, Notre Dame J. Formal Logic 18, 243-247. pdf
- 1977. Binary consistent choice on triples, Notre Dame J. Formal Logic 18, 310-312. pdf
- 1982. Solving algebraic problems in propositional logic by tableaux, Archiv. f. Math. Logik u. Grundl. 22, 187-190.
- 1982. Partition principles for problems of finite character, Reports on Math. Logic 14, 23-28.
- 1983. Compactness via prime semilattices, Notre Dame J. Formal Logic 24, 199-204. pdf
- 1986. Defective colorings of graphs in surfaces (with L. Cowen and D. Woodall), J. Graph Theory 10, 187-195. pdf
- 1990. Two hypergraph theorems equivalent to BPI, Notre Dame J. Formal Logic 31, 232-240. pdf
- 1991. Hypergraph satisfiability, Reports on Math. Logic 25, 113-117.
- 1991. Some conjectures related to the four color conjecture, Graph Theory Notes, New York Acad. Sci., 20, 40-41.
- 1992. Combinatorial analytic tableau, Reports on Math. Logic 27, 29-39.
- 1993. Breakup: a preprocessing algorithm for testing cnfs for satisfiability (with K. Wyatt), Notre Dame J. Formal Logic 34, 602- 606. pdf
- 1993. Some connections between set theory and computer science, Lecture Notes in Computer Science 713, 14-22. pdf
- 1996, A compactness theorem for linear equations (with W. Emerson), Studia Logica,57, 355-357.
- 1998. On finding k4(k3 < x) (with W. Emerson), Graph Theory Notes, New York Acad. Sci., 34, 27-31.
- 1998. Mathematica Plays Games, (with R. Dickau), Mathematica in Education and Research 7, No. 3, 5-10.
- 1998. A compactness theorem for infinite constraint satisfaction, Reports on Math. Logic, 32, 97-108. pdf
- 1999. Inversion and Neighborhood Inversion in Graphs (with S. Hechler, J. Kennedy and A. Ryba), Graph Theory Notes of New York, 37, 37-41.
- 2000. The lights out puzzle (with J. Kennedy), Mathematica in Education and Research, 9, No. 1, 28-32. pdf
- 2001. Discovering Mathematics with Mathematica (with J. Kennedy), Erudition Books.
- 2001. Property S, Reports on Math. Logic, 35, 61-74 pdf.
- 2002. Graph coloring compactness theorems equivalent to BPI (with S.H.Hechler and P.Mihok), Scientiae Mathematicae Japonicae, 56, no.2, 213-223 pdf file .
- 2004. G-free colorability and the Boolean prime ideal theorem (with S.H.Hechler), Scientiae Mathematicae Japonicae, 59, no.2, 257- 263 pdf.
- 2005. Implementing the Davis-Putnam Algorithm in Mathematica (with Mahmuda Huq and Weldon MacDonald), Mathematica in Education and Research, 10, No.2, 46-55. pdf
- 2007. Odd neighborhood transversals on grid graphs (with S.H.Hechler, J.Kennedy, A.Steinberg), Discrete Math., 307 (17-18), 2200 - 2208. pdf
- 2007. Davis-Putnam style rules for deciding Property S (with A. Kolany), Fund. Inform., 79(1-2), 5 - 15.pdf
- 2008. Totally Greedy Coin Sets and Greedy Obstructions (with L.J. Cowen and A. Steinberg), Electronic J. Combinatorics, 15(1), #R90. pdf
- 2009. Generalized Davis-Putnam and satisfiability problems in mathematics, Logic J. of the IGPL(2010), 18(3), 456-463. pdf
- 2009. 2-CNFs and Logical Embeddings, Studia Logica, 93, No. 1, 15-19.pdf
- 2010. Slides. Davis-Putnam: A Combinatorial Approach. pdf
- 2012. A Method for Constructing Minimally Unsatisfiable CNFs. pdf . The Mathematica program used in the paper is available here.
- 2013. Using Boolean Computation to Solve Some Problems from Ramsey Theory, The Mathematica Journal, 2013. dx.doi.org/doi:10.3888/tmj.15-10. pdf
- 2015. Deleting Edges from Ramsey Minimal Examples, Amer. Math. Monthly, August-September, 681-683. dx.doi.org/10.4169/amer.math.monthly.122.7.681 pdf
- Adaptive Fault Diagnosis using Self-Referential Reasoning, to appear. pdf
My daughter Lenore, who is a Mathematician at Tufts has her page here .
My daughter Minda, who is a violin teacher has her web page here .
An introduction to programming two person impartial games in Mathematica, together with several examples can be found here.