Achieving completeness: from constructive set theory to large cardinals

This thesis is an exploration of several completeness phenomena, both in the constructive and the classical settings. After some introductory chapters in the first part of the thesis where we outline the background used later on, the constructive part contains a categorical formulation of several constructive completeness theorems available in the literature, but presented here in an unified framework. We develop them within a constructive reverse mathematical viewpoint, highlighting the metatheory used in each case and the strength of the corresponding completeness theorems. The classical part of the thesis focuses on infinitary intuitionistic propositional and predicate logic. We consider a propositional axiomatic system with a special distributivity rule that is enough to prove a completeness theorem, and we introduce weakly compact cardinals as the adequate metatheoretical assumption for this development. Finally, we return to the categorical formulation focusing this time on infinitary first-order intuitionistic logic. We propose a first-order system with a special rule, transfinite transitivity, that embodies both distributivity as well as a form of dependent choice, and study the extent to which completeness theorems can be established. We prove completeness using a weakly compact cardinal, and, like in the constructive part, we study disjunction-free fragments as well. The assumption of weak compactness is shown to be essential for the completeness theorems to hold.

What Counts Versus What Can Be Counted : The Complex Interplay of Market Orientation and Marketing Performance Measurement

Market orientation (MO) and marketing performance measurement (MPM) are two of the most widespread strategic marketing concepts among practitioners. However, some have questioned the benefits of extensive investments in MO and MPM. More importantly, little is known about which combinations of MO and MPM are optimal in ensuring high business performance. To address this research gap, the authors analyze a unique data set of 628 firms with a novel method of configurational analysis: fuzzy-set qualitative comparative analysis. In line with prior research, the authors find that MO is an important determinant of business performance. However, to reap its benefits, managers need to complement it with appropriate MPM, the level and focus of which vary across firms. For example, whereas large firms and market leaders generally benefit from comprehensive MPM, small firms may benefit from measuring marketing performance only selectively or by focusing on particular dimensions of marketing performance. The study also finds that many of the highest-performing firms do not follow any of the particular best practices identified.