## Research Interests

• Mathematical Logic
• Recursive Function Theory
• Theory of Transfinite Ordinals
• Community Computing

### Expository Article (PostScript Format)

Transfinite Ordinals and Their Notations: For The Uninitiated

### Recent Publications

• Eine rekursive universelle Funktion fur die primitive-rekursiven Funktionen, (Written jointly with W. Nichols, Florida State University.), Zeit f. math Logic u. Grund der Math., Bd. 33 (1987), pp.527-535

A recursive universal function for the primitive recursive functions is constructed. It is based on the characterization of the primitive recursive functions given by Meyer and Ritchie, namely that they are the functions computable by programs in a certain language called LOOP. A by-product is a recursive function that grows faster than any primitive recursive, function. This is a desirable alternative to the so called Ackermann function because the construction is easier to motivate.

• On extending homomorphisms to automorphisms, (Written jointly with W. Nichols at Florida State University) Internat. J. Math. and Math. Sciences, 11 (1988), pp. 231-238

It is shown that for a large class of structures, monic endomorphisms are induced by automorphisms of a larger structure of the same kind. Many garden variety structures are encompassed by this result e.g. groups, rings, vector spaces, fields, metric spaces.

• A natural variant of Ackermann's function, (Written jointly with W. Nichols at Florida State University) Zeit.f. math. Logik u. Grund, 34 (1988), pp. 399-401

Ackermann's function is the classical example of a total computable function which is not primitive recursive. By permuting one clause in the definition of Ackermann's function we arrive at a different function which also has this property, but which in a sense made precise in the paper is the ``right'' way to execute Ackermann's basic strategy.

• A macro program for the primitive recursive functions. (Jointly with W.Nichols, Florida State University, and R. Smith, Duke University), Zeit. f. math. Logik u. Grund, bd37 1991 pp.121-124.

A proof of the existence of a recursive universal function for the class of primitive recursive functions is given. This was first proved by Rosa Peter in 1934. In our proof we view the the problem as one of writing an interpreter for a language whose programs compute primitive recursive functions within a language whose programs compute partial recursive functions. Following an idea in the textbook of Davis and Weyuker, we write this interpreter program ``in macro". We devised a Godel numbering to make things come out simple. The upshot is that our interpreter (in macro) has only nine lines .

• Tallhassee Free-Net: The keystone of a Florida network of community information systems, Journ. of Educational Media and Library Science, Vol 31 No. 4 (1994), pp 364-373.

A discussion of the origin of Tallahassee's community information system, its mission, and progress.

• On Series of ordinals and combinatorics, (jointly with W. Nichols, and J.P.Jones), Mathematical Logic Quarterly, 43 (1997) pp 121-133.

This paper deals mainly with generalizations of results in finite cominatory mathematics to transfinite ordinals. Among other things a formula is derived for summing all the ordinals less than a given ordinal.