The spelling of the word 'oster' is determined by the International Phonetic Alphabet (IPA) phonetic transcription. The word in question is pronounced /ɔstər/. The first syllable is pronounced with an open-mid back rounded vowel sound, represented by the symbol 'ɔ'. The second syllable is pronounced with a schwa sound, represented by the symbol 'ə'. Additionally, the 'r' is pronounced in this word, making the final sound an alveolar tap or 'ɾ' sound. Hence, the correct spelling is 'oster' instead of 'oaster' or any other variant.