1. David Albrecht, Frank A. Bäuerle, John N. Crossley & John S. Jeavons (1998). Curry-Howard Terms for Linear Logic. Studia Logica 61 (2):223 - 235.
    In this paper we 1. provide a natural deduction system for full first-order linear logic, 2. introduce Curry-Howard-style terms for this version of linear logic, 3. extend the notion of substitution of Curry-Howard terms for term variables, 4. define the reduction rules for the Curry-Howard terms and 5. outline a proof of the strong normalization for the full system of linear logic using a development of Girard's candidates for reducibility, thereby providing an alternative to Girard's proof using (...)
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  2. Frank A. Bäuerle, David Albrecht, John N. Crossley & John S. Jeavons (1998). Curry-Howard Terms for Linear Logic. Studia Logica 61 (2):223-235.
    In this paper we 1. provide a natural deduction system for full first-order linear logic, 2. introduce Curry-Howard-style terms for this version of linear logic, 3. extend the notion of substitution of Curry-Howard terms for term variables, 4. define the reduction rules for the Curry-Howard terms and 5. outline a proof of the strong normalization for the full system of linear logic using a development of Girard's candidates for reducibility, thereby providing an alternative to Girard's proof using proof-nets.
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  3. Frank A. Bäuerle & Jeffrey B. Remmel (1994). On Speedable and Levelable Vector Spaces. Annals of Pure and Applied Logic 67 (1-3):61-112.
    In this paper, we study the lattice of r.e. subspaces of a recursively presented vector space V ∞ with regard to the various complexity-theoretic speed-up properties such as speedable, effectively speedable, levelable, and effectively levelable introduced by Blum and Marques. In particular, we study the interplay between an r.e. basis A for a subspace V of V ∞ and V with regard to these properties. We show for example that if A or V is speedable , then V is levelable (...)
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