Klaus Ambos-Spies, Heidelberg Klaus Meer, Cottbus Marat M. Arslanov, Kazan Wolfram Pohlers, Münster Günter Asser, Greifswald Pavel Pudlak, Prague John T. Baldwin, Chicago Andrzej Rosłanowski, Omaha Douglas S. Bridges, Canterbury Jörg Rothe, Düsseldorf Ramon Jansana, Barcelona Wilfried Sieg, Pittsburgh Carl G. Jockusch, Urbana Stephen G. Simpson, State College, PA Alexander Kechris, Pasadena Mar...

In 1987, Craig Squier proved that, if a monoid can be presented by a finite convergent string rewriting system, then it satisfies the homological finiteness condition left-FP3. Using this result, he has constructed finitely presented decidable monoids that cannot be presented by finite convergent rewriting systems. In 1994, Squier introduced the condition of finite derivation type, which is a h...

Connection matrices for graph parameters with values in a field have been introduced by M. Freedman, L. Lovász and A. Schrijver (2007). Graph parameters with connection matrices of finite rank can be computed in polynomial time on graph classes of bounded tree-width. We introduce join matrices, a generalization of connection matrices, and allow graph parameters to take values in the tropical ri...

We introduce the notion of almost finite dimensional representability of algebras and study its connection with the classical finiteness conditions. AMS Subject Classifications: 16N80, 16P99

C. W. Barnes, “Roundoff noise and overflow in normal digital filters,” IEEE Tram. Circuits Syst., vol. CAS-26, pp. 154159, Mar. 19’79. W. L. Mills, C. T. Mullis, and R. A.-Roberts, “Normal realizations of IIR digital filters,” in 1979 IEEE Int. Qnf. Acoustics, Speec,h, Signal Processing Rec., pp. 340-343, Apr. 1979. M. Atjmattd and R. A. Roberts, “Reduced multiplier, low roundoff noise digital ...

Let A be a connected graded noncommutative monomial algebra. We associate to A a finite graphΓ (A) called the CPS graph of A. Finiteness properties of the Yoneda algebra ExtA(k, k) including Noetherianity, finite GK dimension, and finite generation are characterized in terms of Γ (A). We show that these properties, notably finite generation, can be checked by means of a terminating algorithm. ©...

We characterise groups in which every abelian subgroup has finite index in its characteristic closure. In a group with this property every subgroup H has finite index in its characteristic closure and there is an upper bound for this index over all subgroups H of G. For every prime p we construct groups G with this property that are infinite nilpotent p-groups of class 2 and exponent p in which...

An arbitrary renormalizable quantum field theory is considered as finite if its dimensionless couplings conspire to yield at every order of its perturbative expansion no ultraviolet-divergent renormalizations of the physical parameters of the theory. The “finiteness conditions” resulting from these requirements form highly complicated, non-linear systems of relations. A promising type of soluti...

Kierstead showed that every computable marriage problem has a computable matching under the assumption of computable expanding Hall condition and computable local finiteness for boys and girls. The strength of the marriage theorem reaches WKL0 or ACA0 if computable expanding Hall condition or computable local finiteness for girls is weakened. In contrast, the provability of the marriage theorem...

An example of a nitely presented monoid is given that does not satisfy the homo-topical niteness condition FHT, although it satisses both the homological niteness conditions left FP 1 and right FP 1 .tions left FP 1 and right FP 1 .