FINITE H-DIMENSION DOES NOT IMPLY EXPRESSIVE COMPLETENESS

Accepted versio

Functional ecology of soil organisms in tundra ecosystems: Towards the future

The need to understand the functional linkages between Arctic/alpine soil communities and the major soil processes is stressed. Soil organisms are classified into broad functional groups and it is suggested that the functional success of any organism can be defined by its position along four axes, namely population responsiveness, dispersability, ecophysiological flexibility and resource use flexibility. Each of these axes is defined by reference to a spectrum of relevant ecological attributes. The resilience and response of tundra communities to change are discussed and the possible alteration in community structure and function that may result from shifting climate patterns are reviewed. The interrelationship between the spatial distribution patterns of organisms and their dispersability is highlighted and the significance of the thermal environment in moderating the competitive interaction between species is emphasised. The advantages and disadvantages of various approaches to studying the effect of climate change on Arctic/alpine community structure and function are contrasted. In particular, the manipulative experimental approach is distinguished from the comparative approach that makes use of measurements taken along geographical/ecological transects as analogues for climate change

A new species of Heteropsylla Crawford from Ecuador with new host-plant and distribution records for the genus (Homoptera, Psylloidea).

Heteropsylla pulchella spec. nov. aus Ecuador wird beschrieben. Wirtspflanze und Vorkommen von Heteropsylla bidentata, H. cubana, H. truncata, H. obscura und H. spinulosa wurden gegeben.Nomenklatorische Handlungenpulchella Hodkinson & Muddiman, 1993 (Heteropsylla), spec. n.Heteropsylla pulchella spec. nov. is described from Ecuador. Additional host-plant and distribution records are given for Heteropsylla bidentata, H. cubana, H. truncata, H. obscura and H. spinulosa. Nomenclatural Actspulchella Hodkinson & Muddiman, 1993 (Heteropsylla), spec. n

Nymphal taxonomy and systematics of Psylloidea (Homoptera)

Volume: 50Start Page: 153End Page: 30

Provability with Finitely Many Variables

For every finite n>=4 there is a logically valid sentence 'n with the following properties: 'n contains only 3 variables (each of which occurs many times); 'n contains exactly one nonlogical binary relation symbol (no function symbols, no constants, and no equality symbol); 'n has a proof in first-order logic with equality that contains exactly n variables, but no proof containing only n \Gamma 1 variables. This result was first proved using the machinery of algebraic logic developed in several research monographs and papers. Here we replicate the result and its proof entirely within the realm of (elementary) first-order binary predicate logic with equality. We need the usual syntax, axioms, and rules of inference to show that 'n has a proof with only n variables. To show that 'n has no proof with only n \Gamma 1 variables we use alternative semantics in place of the usual, standard, set-theoretical semantics of first-order logic